Fundamental properties of stars from Kepler and Gaia data: parallax offset and revised scaling relations

Data from the space missions Gaia, Kepler, CoRoT and TESS, make it possible to compare parallax and asteroseismic distances. From the ratio of two densities rho(sca)/rho(pi), we obtain an empirical relation f(Delta nu). between the asteroseismic large frequency separation and mean density, which is important for more accurate stellar mass and radius. This expression for main-sequence (MS) and subgiant stars with K-band magnitude is very close to the one obtained from interior MS models by Yildiz, Celik & Kayhan. We also discuss the effects of effective temperature and parallax offset as the source of the difference between asteroseismic and non-asteroseismic stellar parameters. We have obtained our best results for about 3500 red giants (RGs) by using 2MASS data and model values for f(Delta nu). from Sharma et al. Another unknown scaling parameter f(nu max) comes from the relationship between the frequency of maximum amplitude and gravity. Using different combinations of f(nu max) and the parallax offset, we find that the parallax offset is generally a function of distance. The situation where this slope disappears is accepted as the most reasonable solution. By a very careful comparison of asteroseismic and non-asteroseismic parameters, we obtain very precise values for the parallax offset and f(nu max) for RGs of -0.0463 +/- 0.0007 mas and 1.003 +/- 0.001, respectively. Our results for mass and radius are in perfect agreement with those of APOKASC-2: the mass and radius of similar to 3500 RGs are in the range of about 0.8-1.8 M-circle dot (96 per cent) and 3.8-38 R-circle dot, respectively.

Automated summary

By comparing parallax and asteroseismic distances, researchers established an empirical relation between large frequency separation and mean density, leading to more accurate determination of stellar mass and radius. The study also discussed the effects of effective temperature and parallax offset on stellar parameters, obtaining precise values through careful data analysis. Results for red giants were found to be consistent with previous studies, affirming the reliability of the methodology employed.